surfaceInterpolation: New pointLinear scheme

First interpolates from the cells to the vertices and then from the face
vertices to the face centres.  This may be a useful scheme for calculating
gradients on bad/tet meshes when used in conjunction with the Gauss gradient
scheme.

src/finiteVolume/interpolation/surfaceInterpolation/schemes/pointLinear/pointLinear.C

+/*---------------------------------------------------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     |
+    \\  /    A nd           | Copyright (C) 2004-2011 OpenCFD Ltd.
+     \\/     M anipulation  |
+-------------------------------------------------------------------------------
+License
+    This file is part of OpenFOAM.
+
+    OpenFOAM is free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+    FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
+    for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with OpenFOAM.  If not, see <http://www.gnu.org/licenses/>.
+
+\*---------------------------------------------------------------------------*/
+
+#include "pointLinear.H"
+#include "fvMesh.H"
+#include "volPointInterpolation.H"
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+template<class Type>
+Foam::tmp<Foam::GeometricField<Type, Foam::fvsPatchField, Foam::surfaceMesh> >
+Foam::pointLinear<Type>::
+correction
+(
+    const GeometricField<Type, fvPatchField, volMesh>& vf
+) const
+{
+    const fvMesh& mesh = this->mesh();
+
+    GeometricField<Type, pointPatchField, pointMesh> pvf =
+        volPointInterpolation::New(mesh).interpolate(vf);
+
+    tmp<GeometricField<Type, fvsPatchField, surfaceMesh> > tsfCorr =
+        linearInterpolate(vf);
+
+    Field<Type>& sfCorr = tsfCorr().internalField();
+
+    const pointField& points = mesh.points();
+    const pointField& C = mesh.C().internalField();
+    const faceList& faces = mesh.faces();
+    const scalarField& w = mesh.weights().internalField();
+    const labelList& owner = mesh.owner();
+    const labelList& neighbour = mesh.neighbour();
+
+    forAll(sfCorr, facei)
+    {
+        point pi =
+            w[owner[facei]]*C[owner[facei]]
+          + (1.0 - w[owner[facei]])*C[neighbour[facei]];
+
+        scalar at = triangle<point, const point&>
+        (
+            pi,
+            points[faces[facei][0]],
+            points[faces[facei][faces[facei].size()-1]]
+        ).mag();
+
+        scalar sumAt = at;
+        Type sumPsip = at*(1.0/3.0)*
+        (
+            sfCorr[facei]
+          + pvf[faces[facei][0]]
+          + pvf[faces[facei][faces[facei].size()-1]]
+        );
+
+        for (label pointi=1; pointi<faces[facei].size(); pointi++)
+        {
+            at = triangle<point, const point&>
+            (
+                pi,
+                points[faces[facei][pointi]],
+                points[faces[facei][pointi-1]]
+            ).mag();
+
+            sumAt += at;
+            sumPsip += at*(1.0/3.0)*
+            (
+                sfCorr[facei]
+              + pvf[faces[facei][pointi]]
+              + pvf[faces[facei][pointi-1]]
+            );
+
+        }
+
+        sfCorr[facei] = sumPsip/sumAt - sfCorr[facei];
+    }
+
+    tsfCorr().boundaryField() = pTraits<Type>::zero;
+
+    return tsfCorr;
+}
+
+
+namespace Foam
+{
+    makeSurfaceInterpolationScheme(pointLinear);
+}
+
+// ************************************************************************* //

src/finiteVolume/interpolation/surfaceInterpolation/schemes/pointLinear/pointLinear.H

+/*---------------------------------------------------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     |
+    \\  /    A nd           | Copyright (C) 2011-2011 OpenCFD Ltd.
+     \\/     M anipulation  |
+-------------------------------------------------------------------------------
+License
+    This file is part of OpenFOAM.
+
+    OpenFOAM is free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+    FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
+    for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with OpenFOAM.  If not, see <http://www.gnu.org/licenses/>.
+
+Class
+    pointLinear
+
+Description
+    Face-point interpolation scheme class derived from linear and
+    returns linear weighting factors but also applies an explicit correction.
+
+    Uses volPointInterpolation to obtain the field values at the face-points.
+
+SourceFiles
+    pointLinear.C
+
+\*---------------------------------------------------------------------------*/
+
+#ifndef pointLinear_H
+#define pointLinear_H
+
+#include "linear.H"
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+namespace Foam
+{
+
+/*---------------------------------------------------------------------------*\
+                           Class pointLinear Declaration
+\*---------------------------------------------------------------------------*/
+
+template<class Type>
+class pointLinear
+:
+    public linear<Type>
+{
+    // Private Member Functions
+
+        //- Disallow default bitwise copy construct
+        pointLinear(const pointLinear&);
+
+        //- Disallow default bitwise assignment
+        void operator=(const pointLinear&);
+
+
+public:
+
+    //- Runtime type information
+    TypeName("pointLinear");
+
+
+    // Constructors
+
+        //- Construct from mesh
+        pointLinear(const fvMesh& mesh)
+        :
+            linear<Type>(mesh)
+        {}
+
+
+        //- Construct from mesh and Istream
+        pointLinear
+        (
+            const fvMesh& mesh,
+            Istream&
+        )
+        :
+            linear<Type>(mesh)
+        {}
+
+
+        //- Construct from mesh, faceFlux and Istream
+        pointLinear
+        (
+            const fvMesh& mesh,
+            const surfaceScalarField&,
+            Istream&
+        )
+        :
+            linear<Type>(mesh)
+        {}
+
+
+    // Member Functions
+
+        //- Return true if this scheme uses an explicit correction
+        virtual bool corrected() const
+        {
+            return true;
+        }
+
+        //- Return the explicit correction to the face-interpolate
+        virtual tmp<GeometricField<Type, fvsPatchField, surfaceMesh> >
+        correction
+        (
+            const GeometricField<Type, fvPatchField, volMesh>& vf
+        ) const;
+};
+
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+} // End namespace Foam
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+#endif
+
+// ************************************************************************* //